On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
On the numerical condition of algebraic curves and surfaces 1. Implicit equations
Computer Aided Geometric Design
Condition numbers of a nearly singular simple root of a polynomial
Applied Numerical Mathematics
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Theoretical Computer Science - Algebraic and numerical algorithm
The computation of multiple roots of a polynomial
Journal of Computational and Applied Mathematics
A unified approach to resultant matrices for Bernstein basis polynomials
Computer Aided Geometric Design
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The numerical condition of the degree elevation operation on Bernstein polynomials is considered and it is shown that it does not change the condition of the polynomial. In particular, several condition numbers for univariate and bivariate Bernstein polynomials, and their degree elevated forms, are developed and it is shown that the condition numbers of the degree elevated polynomials are identically equal to their forms prior to degree elevation. Computational experiments that verify this theoretical result are presented. The results in this paper differ from those in [Comput. Aided Geom. Design 4 (1987) 191-216] and [Comput. Aided Geom. Design 5 (1988) 215-252], where it is claimed that degree elevation causes a reduction in the numerical condition of a Bernstein polynomial. It is shown, however, that there is an error in the derivation of this result.